Figure below shows a plot of the potential energy as a function of x for a particle moving along the x-axis. Which of the following statement(s) is/are true ?

1. a, c and d are points of equilibrium
2. a is a point of stable equilibrium
3. b is a point of stable equilibrium
4. All of the above

1 and 2

At a, b c and d : \(\frac{dU}{dx} = 0 \Rightarrow\) These points are the points of equilibrium.

At a and c : \(\frac{d^2U}{dx^2} > 0\ \Rightarrow \) These points are points of stable equilibrium.

At b and d : \(\frac{d^2U}{dx^2} < 0\ \Rightarrow \) These points are points of unstable equilibrium.